parts Definition and 817 Threads

Homework Statement integral of ln(2x +1) Homework Equations I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit...

Homework Statement If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx. 2. Homework Equations and attempt at solution I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get...

Homework Statement Integrating 1/xlnx by parts... Homework Equations Find the integral of 1/xlnx The question asks to solve by substitution, which I can do and results in ln(ln(x)) + c It then asks to compute using integration by parts, and then to explain how it can be true (because...

Homework Statement A plane of a mass 5000 kg moving horizontally in 150 m/s break into two parts 2000 kg and 3000 kg because of a internal explosion. If the bigger part be thrown away with a 400 m/s relative to other part to opposite direction of previous moved direction before explosion...

Homework Statement [/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture1.jpg The attempt at a solution[/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/100_0635.jpg Answer I got: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture2.jpg I thought my...

Homework Statement Integrate the following by parts twice \int_{a}^{b}\frac{d}{dr}(r\frac{dT(r)}{dr})\psi(r)dr and show that it can be written as -\lambda^2\bar{T} , where \bar{T}=\int_{a}^{b}r\psi(r)T(r)dr and the function \psi satisfies the following equation...

Homework Statement Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y=e^x and the line x=ln13 about the line x=ln13. Homework Equations The Attempt at a Solution I'm not really sure as to how to do...

Just working through a problem Acheson's book (From Calculus to Chaos) if anyone knows it.. eq 8.6 in this book.. As he's working through the problem he makes the step of this: m\int_{t_{1} }^{t_{2}} \left( \dot{y}_{\scriptscriptstyle A }\dot{\eta} - g\eta \right)\,dt (1) to...

The number of partitions of an even number 2N into N parts appears to be equal to the number of partitions of N. Is this known? If so: Can anyone provide a reference of the corresponding proof? Thanks in advance for any information on this.

Integration by parts - Exponential distribution Homework Statement Solve the following definite integral: \int^{\infty}_{0} \frac{1}{\lambda} x e^{-\frac{x}{\lambda}} dx I'm asked to solve this integral. The solution is \lambda, although I'm not sure how this was done. Homework...

Homework Statement Hi all! I seem to be having trouble doing integration by parts. I seem to have a pretty clear picture of the steps I need to do but something seems to always trick me. Usually I would ask my prof but she is away for a week. I use the formula: uv - ∫vdu = given...

Hello; This is not a homework question, but something I was wondering about solving difference equations. For example, how would I solve the following difference equation; F_{n} = 2F_{n - 2p + 5} + 6p - 17; n, p \in \mathbb N Since it has homogeneous and inhomogeneous parts together (and two...

I am struggling to understand the proof for integer parts of real numbers. I have used to mean less than or equal to because I could not work out how to type it in. I need to show that: ∃ unique n ∈ Z s.t. nx<n+1 The proof given is the following: Let A={k∈Z : kx} This is a...

Hi all I don't know If this is the suitable section for this post.. but at all.. let's see if anybody can make me understand this :):) You all know of course J.J. Thomsons's three CRT experiments... The first one was aiming to prove that the appearing rays and the negative charges...

\[\int e^x(x+1)\ln x \ dx \] Not sure how to approach this. Would I have to multiply it out first?

The past few examples in my review book demonstrated u-substitution to integrate trig functions. The example I'm on suddenly shows integration by parts. The book doesn't explain why this method is used over u-sub. \int[SIZE="4"]sec3x dx In what situation am I supposed to use one method over...

Homework Statement Evaluate the double integral. Homework Equations integral by part: uv - integral of v*du The Attempt at a Solution I wrote out my works. And I am just stuck at the x integration... Please click on the links to see the pictures. I don't want to resize it which may...

Homework Statement Hi there. I'm confused about this exercise. It asks me to solve the integral using integration by parts. And the integral is: \displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx The Attempt at a Solution What I did: u=3x du=3dx dv=cos(\displaystyle\frac{x}{2})...

Homework Statement Using summation by parts, find Sum[n/3^n]. Homework Equations Sum[a_k*b_k] = s_n*b_(n+1) - Sum[s_k(b_(k+1)-b_k] The Attempt at a Solution Let a_k = 1/3^k and b_k = k. Then b_(k+1)-b_k = 1. But what is s_k? I know that it is 1/3 + 1/3^2 + 1/3^3 + ... but...

Series convergence "by Parts Supose: \sum c_n = \sum (a_n+b_n) (*1) \sum a_n is conditionaly convergent (*2) \sum b_n is absolutly convergent (*3) And I have seen this proof: [Proving \sum c_n is conditionally convergent] From (*1) and (*2) \Rightarrow \sum c_n its...

¿Are conserved the spin and orbital parts of the angular momentum? For example , we have a particle decay into two photons, and you want to see if the angular momentum is conserved: J(total angular momentum)=S(spin)+L(orbital) The question is: -¿only total J is conserved? (and s or l...

Homework Statement Evaluate the indefinite integral. ∫(x + 3)/(x^2+6x) dx Homework Equations This is an online homework prob. that covers sections integration by parts and substitution in indefinite integrals. it looks to me that it fits into the formula ∫udv=uv-∫vdu if you change...

Hi all, I have an exceptionally basic question, taken from P21 of Zee. Eq. 14 is Z=\int D\psi e^{i\int d^4x(\frac{1}{2}[(\partial\psi )^2-m^2\psi^2] + J\psi)} The statement is then made that 'Integrating by parts under the \int d^4x' leads to Eq. 15: Z=\int D\psi e^{i\int...

Homework Statement Gosh I've been asking a lot of questions lately...anyways... I tried this question two separate times and couldn't manage to figure out where i went wrong... \int e^{-x}cos2x dx Homework Equations uv - \int v du = \int u dvdx The Attempt at a Solution let u = e^{-x}...

1. Fluorine compounds are added to water, the concentration being 0.90 ppm. a. What amount of fluoride present 1.0g of water? Solution- (just need to know what the number mean) Divided 0.90 pm by 1,000,000, which I assume is the grams of substance per kilogram? Then divided that...

Homework Statement find ⌠cotx using integration by parts with using u= 1/sinx and dv= cosx Homework Equations cotx=cosx/sinx The Attempt at a Solution u= 1/sinx and dv= cosx dx du = -cotxcscx dx v= sinx ⌠udv = 1 + ⌠sinx cotx cscx sinx and cscx cancel out. ⌠cotx = 1 +...

So, in my class we are learning how to use the tabular method to solve an integration by parts problem... but what happens if the two parts of the integral continuously repeat? The example I have in mind is \int e^x sin(x) dx. I know how to solve this using repeated integration by parts...

Homework Statement By integrating by parts , show that \int \frac{1}{1-x^2}dx=\frac{x}{1-x^2}-\int \frac{2x^2}{(1-x^2)^2}dx Homework Equations The Attempt at a Solution I don see which is u and v.

How do I integrate the following: \int_0^\infty r e^{-ar} \sin{(Kr)} dr i tried writing r e^{-ar} = -\frac{d}{da} e^{-ar} and using integration by parts but i couldn't get anywhere. any ideas?

Homework Statement ∫e^-x cos(2x)dx Homework Equations I'm trying integration by parts and I set u=e^-x and dv=cos(2x) The Attempt at a Solution I got to where ∫udv= (e^-x)(1/2 sin(2x))+1/2∫sin(2x)e^-x I am trying to run through a second time and I'm a little stuck

Homework Statement ∫〖e^√x/√x dx〗 would this be a u substitution or a substitution by parts? Homework Equations The Attempt at a Solution

Homework Statement the question : integrate the following : integration of d(y/x) = integration of(c cos x/x^2) dx , where c is a constant Homework Equations integration of d(y/x) = integration of(c cos x/x^2) dx y/x = c integration of (c cos x/x^2) dx (*) = c(x^-2...

Homework Statement Can anyone tell me which one is right (LIPET or LIATE)? Also, in trig, which one come first? sin,cos or tan? thxHomework Equations The Attempt at a Solution

Homework Statement evaluate the integral cos^-1 2x dx? Homework Equations The Attempt at a Solution let u = arc cos du = -1 / (sqrt 1-x^2) dv = 2x v= x^2 arc cos * x^2 - the integral of -x^2 / (sqrt 1-x^2) then i don't know what to do

Im trying to come up with a sort of diagram you could call it, of a black hole and all its "parts" for example i know there's the event horizon, ergosphere, the jets that come out of the poles. And any other helpful info. about black holes and there classification, like there's rotating ones...

Homework Statement Let I_{n} = \int^{2}_{0} x^{n}e^{x} dx where n is a positive integer. Use integration by parts to show that 2^{n}e^{2} - nI_{n-1} By first finding I_{1} = \int ^{2}_{0} xe^{x} dx find I2 and I3.Homework Equations I'm sure your all aware of the formula for Int by...

Homework Statement Find \int^{1}_{0} (x^{2} - 3x + 1)e^{x} dxHomework Equations Let f =(x^{2} - 3x + 1) [tex g = e^{x}[/tex] f' = 2x - 3 \int (g) dx = e^{x} The Attempt at a Solution We are going to have to use intergation by parts twice as the degree of the first function (f) is 2...

"Distributions" and Intergration by Parts Homework Statement Has it been proven that it is ok to use Integration by parts on "Distributions" like Dirac Delta functions inside an integration? Homework Equations Need to figure out how to write integral signs and Greek alphabet symbols...

Hi, Can you tell me if I am on the right track with this problem. Thanks in advance. Homework Statement Evaluate the integral using integration by parts Homework Equations ln(2x + 1)dx The Attempt at a Solution ln(2x + 1)dx = ln(2x + 1) * 1dx Let U = ln(2x + 1)...

\int_0^{infinity} \ e^{-s*t}*t*cos(t) dt I tried integration by parts with u=t*cost and dv=e^(-s*t) but that didn't get anywhere. I then tried: \L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt but again nothing was working. This is a Laplace Transformation where ft=t cos(t)

Integration By Parts? Homework Statement int.arctan(2x)dx Homework Equations Integration By Parts The Attempt at a Solution In the attached image is the original problem with the ansewer I came up with using integration by parts and then a v=sub. later in the problem I did not...

Homework Statement Homework Equations The Attempt at a Solution What I am unsure of is how to find the derivative of u. Since the original integral is integrating with respect to y, should I be finding the derivative of u with respect to y, and treat the x's as contants?

Homework Statement Use integration by parts to prove the reduction formula: http://img214.imageshack.us/img214/1234/24206074.jpg Homework Equations The Attempt at a Solution what confuses me about this question is that its not in the form sqrt(a2 + x2) but its in ^n instead of...

Homework Statement Here is a question I'm struggling with. I encountered it in a paper, and although a solution is provided I'm not so sure I understand where they're coming from. Homework Equations \int_{r_1}^{r_2} \overline{v}\frac{1}{r}\frac{d}{dr}(r\frac{du}{dr})rdr where...

Homework Statement intergral from pi to 0. of (sin(3t)dt)^4 The Attempt at a Solution okay so i know how to do this but when i tried substitution putting 3t=u and (1/3)du= dt i always came with the the wrong coefficient at the end with the answer and so i would multiply it...

Parts, componets, and things that "do stuff" Hi guys! I'm actually an electrical engineering student, but I figured this might be more applicable here. I'm trying to find websites that are good for ordering parts such as bearings, shafts, gears, chains, cogs, and more. I'm planning on...

Homework Statement integral tan-1x dx i am supposed to integrate this by parts Homework Equations The Attempt at a Solution integral tan-1x dx = integral cosx/sinx dx u=cos x, du=-sin x dx v=ln sin x, dv= sin-1x dx integral cosx/sinx dx= cosx ln(sinx) - integral[ ln(sinx)(-sinx) dx] is...

Homework Statement I'm getting different results when choosing my u & dv for Integration by Parts on the following integral: \int 2x^3 e^x^2 dx (Note, the exponent on 'e' is x^2) This yields the correct solution: u = x^2 dv = 2x e^x^2 dx du = 2xdx v = e^x^2 However, I have tried using...

Homework Statement The method to use to integrate the function is up to us. The choices are: 1) U-substitution 2)Integration by Parts 3)Trigonometric integrals 4)Trigonometric substitution 5)Partial fraction Homework Equations According to me, the best way to do it is to use...

Homework Statement Use the method of cylindrical shells to find the volume generated by rotating the region R bounded by the curves y=e1.6 x, y=e−1.6 x and x=0.6 about the y-axis. Homework Equations V=$\displaystyle \Large \int _a^c 2pix (yt - yb) dx$ The Attempt at a Solution...